The easiest way I know of learn a new song is simply this: Play. Sleep. Repeat.

This is supposed to work for learning anything new, actually. Dreams are believed to be your brain's way of reorganizing the new information it received during the day into lasting memories. Or so goes the theory. Give it a try, it has worked for me!

This is interesting. Along the same lines I found an interesting story (this is not my own, I am paraphrasing someone else's...n/m):

The phrase "use it or lose it" isn't just for muscles. Scientists studying how the brain works have made discoveries that indicate this saying also holds true for our minds.

They have discovered something interesting about mastering difficult tasks: the better you get at doing something difficult, the less brainpower it takes. Piano teachers have always known this, the brain uses less fuel as it becomes more accomplished and as challenges are increased. The relationship between practice and performance is obvious to musicians who know that it gets easier to do more complex things as you become a better player. How do you get to Carnegie Hall? "Practice. Practice. Practice!"

That is why it is so important to hang in there in the early stages of learning a new skill even if you feel awkward and frustrated. If you do the payoff will be there for you down the road and it will get a whole lot easier.

When learning a new song (especially the more complex ones) you don't need to play every single note necessarily. A few shortcuts (skipping notes here or there) make songs easier to learn and play and will often be imperceptible.

Once you play it enough your fingers will just know what to do without even thinking about it (muscle memory), and once that happens, you can make the song more complex by adding in the missing notes or even improvising your own.

I find that learning a song one hand at a time works best. I normally start with the left hand, which is often the simpler and more repetitious melodies, and once I have that memorized, then start learning the right hand.